Born scattering of long‐period body waves

The Born approximation is applied to the modelling of the propagation of deeply turning long‐period body waves through heterogeneities in the lowermost mantle. We use an exact Green's function for a spherically symmetric earth model that also satisfies the appropriate boundary conditions at internal boundaries and the surface of the earth. The scattered displacement field is obtained by a numerical quadrature of the product of the Green's function, the exciting wavefield and structural perturbations. We study three examples: scattering of long‐period P waves from a plume rising from the core–mantle boundary (CMB), generation of long‐period precursors to PKIKP by strong, localized scatterers at the CMB, and propagation of core‐diffracted P waves through large‐scale heterogeneities in D″. The main results are as follows: (1) the signals scattered from a realistic plume are small with relative amplitudes of less than 2 per cent at a period of 20 s, rendering plume detection a fairly difficult task; (2) strong heterogeneities at the CMB of appropriate size may produce observable long‐period precursors to PKIKP in spite of the presence of a diffraction from the PKP ‐B caustic; (3) core‐diffracted P  waves ( P diff ) are sensitive to structure in D″ far off the geometrical ray path and also far beyond the entry and exit points of the ray into and out of D″; sensitivity kernels exhibit ring‐shaped patterns of alternating sign reminiscent of Fresnel zones; (4) P diff also shows a non‐negligible sensitivity to shear wave velocity in D″; (5) down to periods of 40 s, the Born approximation is sufficiently accurate to allow waveform modelling of P diff through large‐scale heterogeneities in D″ of up to 5 per cent.